Proper grey water disposal is an essential LNT Skill. The system you use really depends on where you are camping and the conditions there.

I am trying to find an image of a simple grey water system for camp, but cannot seem to find one (Maybe check the Field Book to Canadian Scouting). However, at its simplest a grey water system separates food particles and fats from the water. Prop up a small plastic bag over a small hole, fill the plastic bag with dead leaves and grass, cut a small hole in a corner of the bag and gently pour your grey water through. When done, dispose of the leaves and grass (burn them, broadly scatter far away from open water and camp, or carry them out) and cover up your hole.

We copied the Girl Guide variation - a surgical cap or J-cloth over a 5 gal. bucket for standing camps, over an ice cream bucket for lightweight camps. First step is to scrape all food particles into garbage before washing dishes.

While I attempt to follow the 7 Principles of LNT, I am not a fundamentalist about it. In my part of the world, digging up a small bit of sod for grey water disposal would not be a concern. However, there are some environs where this practice would be very damaging. So yes, point taken. Step one is to assess your environment.

I do like the bucket methods you suggested! I think that would work very well for a standing camp with a larger group and easily modified for a patrol on a light weight camp. Here is the method I use when lightweight backpacking:

Don't dig a hole - and at any camp I've been to, we use the large gallon bucket and filter out food, scrape thoroughly before washing, etc. and where allowed, the grey water goes into the kybo.

But the requirement is specific: I can use a shovel to build a camp greywater sump pit and close the pit when finished. I also spotted this and flagged it to another Scouter: when could this be done, as it's usually not what we do? Of course, the Scout could just complete most as he can, and then complete Level 4 without ever being awarded Level 3...